Question

Will you help me?

Answer 1

Use Pytagoras on the triangle AEC, and show that `90r=150^2+45^2`. Calculate r from this.

Explanation:

I don't think I will do all the math for you, but remember that in a right triangle, `s_1^2+s_2^2=h^2`
where `s_1` and `s_2` are the sides, and h is the hypotenus.

In the right triangle AEC you have
`s_1=AC=150`
`s_2=CE=r-45`
`h=AE=r`

Therefore, from Pytagoras:
`r^2=150^2+(r-45)^2 =150^2 + r^2 - 90r +45^2`
From this it follows that
`90r=150^2+45^2`

From this it should be easy to find your answer, so I'll leave you here.